Nomenclature: Yang-Mills theory vs Gauge theoryYes, that's why I said "we usually think of..." and that whole specific example I gave of gravity not being a Yang-Mills theory... But the point is there's not well-defined agreed upon definition of what a Yang-Mills theory is--it's just a gauge theory that we usually think of as being SO or SU, which is exactly what I said. And I have certainly heard lattice people call their theories Yang-Mills, btw. I think the terminology is probably more of a cultural one than a definitional one, anyway.

Does the HUP alone ensure the randomness in QT?He discusses this somewhat carelessly on p.118 of my edition (2nd) just above problem 3.17 at the end of ch. 3.5. One can be more careful, though. If you look in a more advanced book you should be able to find a real discussion of this?

Apr12

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Does the HUP alone ensure the randomness in QT?@jaskey13 the analogues of conservation laws apply to measured values, because they come from symmetries of the Hamiltonian, which are respected at the quantum level. This means they also apply to Ehrenfest-type statements about expectation values. I believe Griffiths discusses conservation laws somewhere at least a little?

Apr12

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Does the HUP alone ensure the randomness in QT?@jaskey13 I don't think it's right to say that about momentum and position. They're very real things quantum mechanically, we still have quantum mechanical analogues of, e.g., conservation of momentum and energy, despite the fact that they are not "well-defined" in a classical sense. In fact, if you look at how to derive the Schroedinger equation, you replace operators into E = p^2/2m and act this on a function, usually as a function of position, which is surely taking all of these properties very seriously and fundamentally!

Apr10

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Does the HUP alone ensure the randomness in QT?It's true that the uncertainty principle is derived, but what you say in your third paragraph doesn't make much sense. There's not really anything classical about observables. In fact, they act very non-classically since they have nontrivial commutation relations with other things. Observables are operators on the Hilbert space of states, and "project" out (in some sense) the information contained in the state vector you're looking for. The "classical" things are more related to expectation values, not the operators. I think Griffiths discuses this somewhere in the exercises.